Factors & Multiples — Quiz 3

Questions in this quiz (14)

1. For the numbers 36 and 60, calculate the least common multiple divided by the greatest common factor.

   • 5
   • 9
   • 15
   • 4

2. The number 9 is a positive integer with exactly three factors: 1, 3, and 9. If m is the next positive integer that also has exactly three factors. What is the sum of the three factors of m?

   • 30
   • 31
   • 32
   • 29

3. If $$a$$ is a factor of $$36$$ and $$b$$ is a factor of $$54$$, which of the following could NOT be the product of $$a$$ and $$b$$?

   • 972
   • 216
   • 108
   • 1

4. Consider all products $$pq$$, where $$p$$ is divisible by 6 and $$q$$ is divisible by 14. Which of the following is not a factor of $$pq$$?

   • 12
   • 18
   • 42
   • 84

5. A group of friends orders pizza after a party. The host wants to order enough slices so that each friend receives an equal number without remainder. If either 6, 9, or 12 friends will be eating pizza and if slices cannot be subdivided, what is the least possible number of slices that should be ordered?

   • 18
   • 36
   • 54
   • 72

6. What are the possible values of $$a$$ such that $$ab^2 = 72$$ and $$a, b$$ are integers?

   • $$2, 3$$
   • $$2, 4$$
   • $$1, 12, 72$$
   • $$1, 3, 12, 72$$

7. A number z is produced by multiplying a, which is divisible by 12, and b, which is divisible by 18. All of the following whole numbers must be factors of z EXCEPT:

   • 3
   • 9
   • 36
   • 56

8. A positive integer $$k$$ is less than 400 and is a multiple of 8. When $$\frac{k}{400}$$ is written as a decimal number, what is the minimum number of digits to the right of the decimal point?

   • 1
   • 2
   • 3
   • 4

9. When $$y$$ is divided by $$5$$, the remainder is $$2$$. When $$y$$ is divided by $$8$$, the remainder is $$6$$. What is the smallest possible value of $$y$$?

   • $$22$$
   • $$36$$
   • $$42$$
   • $$54$$

10. If an integer is divisible by 8 and by 12, then the integer must be evenly divisible by which of the following?I. 16II. 24III. 48

    • I, II
    • II
    • II, III
    • I, III

11. Samantha has a 54 cm long yellow ribbon and a 72 cm long green ribbon. She wants to cut both ribbons into smaller pieces of equal length. Each piece, whether from the yellow or green ribbon, must be the same length. What is the greatest possible length of each piece?

    • 18
    • 32
    • 36
    • 16

12. Positive integers $$m$$ and $$n$$ have no common factor except 1. In addition, $$n = 4(m - n)$$Find the values of $$m$$ and $$n$$.

    • $$m = 2, n = 1$$
    • $$m = 4, n = 2$$
    • $$m = 1, n = 2$$
    • $$m = 5, n = 4$$

13. Four bells toll together at the intervals of $$12$$, $$18$$, $$24$$, and $$36$$ minutes. If they start now tolling together, after what time will they next toll together?

    • 36
    • 63
    • 72
    • 42

14. If $$a$$ and $$b$$ are positive integers such that the greatest common factor of $$a^2b$$ and $$ab^3$$ is $$36$$, then which of the following could $$b$$ equal?

    • 6
    • 9
    • 18
    • 36